In this study, we examine some properties of Salkowski curves in $\mathbb{E}^{3}$. We then make sense the angle $(nt)$ parametric equation curves. provide relationship between and binormal vector Darboux Through angle, obtain unit direction curve. Finally, calculate modified orthogonal frames with both curvature torsion give relationships Frenet frame

If there is an order-preserving group isomorphism from a directed abelian group G with a finitely generated positive cone G+ onto a simplicial group, then G is called a semisimplicial group. By factoring out the torsion subgroup of a unital group having a finite unit interval, one obtains a semisimplicial unital group. We exhibit a representation for the base-normed space associated with a semi...

In the title compound, C(22)H(22)N(2), the asymmetric unit contains one half-mol-ecule. A crystallographic inversion centre is located at the mid-point of the bond common to both rings, in the central naphthalene unit. Quantum-mechanical ab initio calculations on the isolated mol-ecule showed that the minimum energy configuration occurs when the naphthalene ring system and the pyrrolyl groups d...

In the title compound, C15H15N3O2S, the central C-N-N-C unit has an anti conformation [torsion angle = -170.17 (15)°]. The phenyl substituent is oriented perpendicular to this unit [dihedral angle of 89.2 (1)°], whereas the substituted ring is rotated out of this plane by only 18.86 (17)°. In the crystal, mol-ecules are linked by pairs of N-H⋯S hydrogen bonds into inversion dimers that are furt...

The title compound crystallizes in the orthorhombic, noncentrosymmetric space group Pna2(1) with a = 10.241(11), b = 12.903(12), c = 9.312(9) A and with one formula unit per asymmetric unit. The stereochemically comparable torsion angles of the cation of 1 and of acetylcholine chloride are analogous. In the crystal structure the trimethylammonio methyl group is surrounded by three anions in the...

The asymmetric unit of title compound, C12H12N2O4, consists of two independent mol-ecules. In each mol-ecule, the oxadiazine ring has a flattened envelope conformation with the methyl-ene C atom as the flap atom, and the eth-oxy-carbonyl unit is in a syn-periplanar conformation with respect to the oxadiazine ring as indicated by O-C-C=O torsion angles of 1.9 (4) and 2.5 (4)°. The dihedral angle...

It is shown that any torsion unit of the integral group ring ZG of a finite group G is rationally conjugate to a trivial unit if G = P o A with P a normal Sylow p-subgroup of G and A an abelian p′-group (thus confirming a conjecture of Zassenhaus for this particular class of groups). The proof is an application of a fundamental result of Weiss. It is also shown that the Zassenhaus conjecture ho...

Torsion theories are here extended to categories equipped with an ideal of 'null morphisms', or equivalently a full subcategory of 'null objects'. Instances of this extension include closure operators viewed as generalised torsion theories in a 'category of pairs', and factorization systems viewed as torsion theories in a category of morphisms. The first point has essentially been treated in [15].

wandering spleen, defined as a spleen without its usual peritoneal attachments, is a rare entity. we report a 34-year-old woman with acute abdomen due to torsion of the long vascular pedicle of a wandering spleen, displaced in the abdominal cavity, and infarction of the spleen. wandering spleen was diagnosed by ultrasound and computed tomography (ct) scan, and was managed by splenectomy in this...

0